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QOTD # 14 The perimeter of a flat rectangular lawn is 42 met

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QOTD # 14 The perimeter of a flat rectangular lawn is 42 met [#permalink] New post 10 Sep 2016, 01:50
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The perimeter of a flat rectangular lawn is 42 meters. The width of the lawn is 75 percent of its length. What is the area of the lawn, in square meters?

    A) 40.5
    B) 96
    C) 108
    D) 192
    E) 432

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Question: 14
Page: 179
[Reveal] Spoiler: OA

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Re: QOTD # 14 The perimeter of a flat rectangular lawn is 42 met [#permalink] New post 10 Sep 2016, 01:52
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Explanation

Let s and t be the width and length, in meters, of the lawn, respectively. Then the perimeter is 25 + 2t meters, so that 2s + 2t = 42. Also, the relationship between the width and the length can be translated as 5 = 0.75t. Substituting 0.75t for s in the equation for the perimeter yields 42 =
2(0.75t) + 2t = 3.5t. So \(t = \frac{42}{3.5}\) and 5 = (0.75)(12) = 9. Since 5t = 108, the area of the lawn is 108 square meters.

The correct answer is Choice C.
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Re: QOTD # 14 The perimeter of a flat rectangular lawn is 42 met [#permalink] New post 19 Sep 2016, 16:50
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Carcass wrote:
The perimeter of a flat rectangular lawn is 42 meters. The width of the lawn is 75 percent of its length. What is the area of the lawn, in square meters?

    A) 40.5
    B) 96
    C) 108
    D) 192
    E) 432




The width of the lawn is 75 percent of its length
In other words, the width is 3/4 times the length.
Let L = the length
This means (3/4)L = the width
Or we can write 3L/4 = the width

The perimeter of a flat rectangular lawn is 42 meters
In other words, 2(length) + 2(width) = 42
So, 2L + 2(3L/4) = 42
Simplify: 2L + 3L/2 = 42
Multiply both sides by 2 to get: 4L + 3L = 84
Simplify: 7L = 84
Solve: L = 12

Since 3L/4 = the width, we know that the width = 3(12)/4 = 9

Area = (length)(width)
= (12)(9)
= 108

Answer:
[Reveal] Spoiler:
C


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Re: QOTD # 14 The perimeter of a flat rectangular lawn is 42 met [#permalink] New post 08 Aug 2017, 09:33
You can get this best lawn mower with bag for this type of lawn because this is the best one
Re: QOTD # 14 The perimeter of a flat rectangular lawn is 42 met   [#permalink] 08 Aug 2017, 09:33
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